umontreal.iro.lecuyer.randvarmulti

Class MultinormalGen

java.lang.Object

umontreal.iro.lecuyer.randvarmulti.RandomMultivariateGen

umontreal.iro.lecuyer.randvarmulti.MultinormalGen

Direct Known Subclasses:

MultinormalCholeskyGen, MultinormalPCAGen

public class MultinormalGen
extends RandomMultivariateGen

Extends RandomMultivariateGen for a multivariate normal (or multinormal) distribution. The d-dimensional multivariate normal distribution with mean vector μ∈R^d and (symmetric positive-definite) covariance matrix Σ, denoted N(μ, Σ), has density

f (X) = exp(- (X - μ)^tΣ^-1(X - μ)/2)/((2π)^d )^1/2,

for all X∈R^d, and X^t is the transpose vector of X. If Z∼N( 0,I) where I is the identity matrix, Z is said to have the standard multinormal distribution.

For the special case d = 2, if the random vector X = (X₁, X₂)^t has a bivariate normal distribution, then it has mean μ = (μ₁, μ₂)^t, and covariance matrix

Σ = []

if and only if Var[X₁] = σ₁², Var[X₂] = σ₂², and the linear correlation between X₁ and X₂ is ρ, where σ₁ > 0, σ₂ > 0, and -1 <= ρ <= 1.

Constructor Summary

Constructors

Constructor and Description
MultinormalGen(NormalGen gen1, int d) Constructs a generator with the standard multinormal distribution (with μ = 0 and Σ = I) in d dimensions.

Method Summary

Modifier and Type	Method and Description
double[]	getMu() Returns the mean vector used by this generator.
double	getMu(int i) Returns the i-th component of the mean vector for this generator.
DoubleMatrix2D	getSigma() Returns the covariance matrix Σ used by this generator.
void	nextPoint(double[] p) Generates a point from this multinormal distribution.
void	setMu(double[] mu) Sets the mean vector to mu.
void	setMu(int i, double mui) Sets the i-th component of the mean vector to mui.

Methods inherited from class umontreal.iro.lecuyer.randvarmulti.RandomMultivariateGen

getDimension, getStream, nextArrayOfPoints, setStream

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MultinormalGen

public MultinormalGen(NormalGen gen1,
                      int d)

Constructs a generator with the standard multinormal distribution (with μ = 0 and Σ = I) in d dimensions. Each vector Z will be generated via d successive calls to gen1, which must be a standard normal generator.

Parameters:

gen1 - the one-dimensional generator

d - the dimension of the generated vectors

Throws:

java.lang.IllegalArgumentException - if the one-dimensional normal generator uses a normal distribution with μ not equal to 0, or σ not equal to 1.

java.lang.IllegalArgumentException - if d is negative.

java.lang.NullPointerException - if gen1 is null.

Method Detail

getMu

public double[] getMu()

Returns the mean vector used by this generator.

Returns:

the current mean vector.

getMu

public double getMu(int i)

Returns the i-th component of the mean vector for this generator.

Parameters:

i - the index of the required component.

Returns:

the value of μ_i.

Throws:

java.lang.ArrayIndexOutOfBoundsException - if i is negative or greater than or equal to getDimension.

setMu

public void setMu(double[] mu)

Sets the mean vector to mu.

Parameters:

mu - the new mean vector.

Throws:

java.lang.NullPointerException - if mu is null.

java.lang.IllegalArgumentException - if the length of mu does not correspond to getDimension.

setMu

public void setMu(int i,
                  double mui)

Sets the i-th component of the mean vector to mui.

Parameters:

i - the index of the modified component.

mui - the new value of μ_i.

Throws:

java.lang.ArrayIndexOutOfBoundsException - if i is negative or greater than or equal to getDimension.

getSigma

public DoubleMatrix2D getSigma()

Returns the covariance matrix Σ used by this generator.

Returns:

the used covariance matrix.

nextPoint

public void nextPoint(double[] p)

Generates a point from this multinormal distribution.

Specified by:

nextPoint in class RandomMultivariateGen

Parameters:

p - the array to be filled with the generated point